On the size of the maximum of incomplete Kloosterman sums

@article{Bonolis2018OnTS,
  title={On the size of the maximum of incomplete Kloosterman sums},
  author={Dante Bonolis},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2018}
}
  • Dante Bonolis
  • Published 26 November 2018
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
<jats:p>Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S030500412100030X_inline1.png" /> <jats:tex-math>$t:{\mathbb F_p} \to C$</jats:tex-math> </jats:alternatives> </jats:inline-formula> be a complex valued function on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href… 
2 Citations
ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS
  • Youness Lamzouri
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2018
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of
The distribution of the maximum of partial sums of Kloosterman sums and other trace functions
In this paper, we investigate the distribution of the maximum of partial sums of families of $m$-periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates

References

SHOWING 1-10 OF 45 REFERENCES
ON THE DISTRIBUTION OF THE MAXIMUM OF CUBIC EXPONENTIAL SUMS
  • Youness Lamzouri
  • Mathematics
    Journal of the Institute of Mathematics of Jussieu
  • 2018
In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as ‘Birch sums’. Our main theorem gives upper and lower bounds (of
Kloosterman paths and the shape of exponential sums
We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums $\text{Kl}_{p}(a)$ , as $a$ varies over $\mathbf{F}_{p}^{\times }$ and as $p$ tends to infinity.
Mean Values of Character Sums
For a non-principal Dirichlet character χ modulo q, Let the Pólya-Vingradov inequality asserts that M(x) < q 1/2 log q see [7]. in the opposite direction it is a trivial consequence of lemma 1 below
Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a
Lower bounds on odd order character sums
A classical result of Paley shows that there are infinitely many quadratic characters $\chi\mod{q}$ whose character sums get as large as $\sqrt{q}\log \log q$; this implies that a conditional upper
On the conductor of cohomological transforms
In the analytic study of trace functions of $\ell$-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological
Gaussian distribution of short sums of trace functions over finite fields
Abstract We show that under certain general conditions, short sums of ℓ-adic trace functions over finite fields follow a normal distribution asymptotically when the origin varies, generalising
The distribution of the maximum of character sums
We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character
Exponential sums and di?erential equations
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential
Colloquium De Giorgi 2013 and 2014
Pierre Cartier: New Developments in Galois Theory.- Enrico Bombieri: The Mathematical Truth.- Alessio Figalli: Quantitative Stability Results for the Brunn-Minkowski Inequality.- Luc Illusie:
...
...